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A store purchased x sweaters for a total price of $750. If it sold all
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07 Dec 2017, 20:20

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Difficulty:

85% (hard)

Question Stats:

50%(02:47) correct 50%(03:18) wrong based on 59 sessions

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A store purchased x sweaters for a total price of $750. If it sold all but four of them, each for $5 more than the average price it paid for a sweater, and in doing so earned a total profit of $30 on the original purchase, how many sweaters did it sell?

Re: A store purchased x sweaters for a total price of $750. If it sold all
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07 Dec 2017, 22:33

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Bunuel wrote:

A store purchased x sweaters for a total price of $750. If it sold all but four of them, each for $5 more than the average price it paid for a sweater, and in doing so earned a total profit of $30 on the original purchase, how many sweaters did it sell?

A. 21B. 24C. 26D. 30E. 35

The answer is 26

X sweaters are purchased for 750 then price per sweater is 750/x

He sold all but 4 means that he sold x-4 for a prices greater than 750/x by 5He earned a profit of 30 So putting the in equation we have

Re: A store purchased x sweaters for a total price of $750. If it sold all
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01 Feb 2019, 17:45

Bunuel wrote:

A store purchased x sweaters for a total price of $750. If it sold all but four of them, each for $5 more than the average price it paid for a sweater, and in doing so earned a total profit of $30 on the original purchase, how many sweaters did it sell?

A. 21B. 24C. 26D. 30E. 35

The average price paid for each sweater is 750/x.

The store sold (x - 4) sweaters for [(750/x) + 5 dollars] each and made a profit of 30 dollars; thus:

(x - 4)[(750/x) + 5] - 750 = 30

(x - 4)[(750/x) + (5x/x)] = 780

(x - 4)(750 + 5x)/x = 780

750x + 5x^2 - 3000 - 20x = 780x

5x^2 - 50x - 3000 = 0

x^2 - 10x - 600 = 0

(x - 30)(x + 20) = 0

x = 30 or x = -20

Since x can’t be negative, x = 30. So the store purchased 30 sweaters and sold 26 of them.